Chapter Four Mechanical Analysis of Soil

4.1 Introduction Mechanical analysis is the determination of the size range of particles present in a soil, expressed as a percentage of the total dry weight.

4.3 Sieve Analysis Sieve analysis consists of shaking the soil sample through a set of sieves that have progressively smaller openings. U.S. standard sieve numbers and the sizes of openings are given in following table:

4.2 Purpose Engineering behavior of soils (such as Permeability , bearing capacity, Compressibility, …etc.) is controlled by grain size , shape and plasticity of soil particles. Soil can range from boulders or cobbles of several centimeters in diameter down to ultrafine‐grained material.

Two methods generally are used to find the particle-size distribution of soil: (1) sieve analysis: for particle sizes larger than 0.075mm in diameter (2) hydrometer analysis: for particle sizes smaller than 0.075 mm in diameter.

To conduct a sieve analysis: 1- Oven-dry the soil and then break all lumps into small particles. 2- The soil then is shaken through a stack of sieves with openings of decreasing size from top to bottom (a pan is placed below the stack). 3- After the soil is shaken, the mass of soil retained on each sieve is determined. 4- Portions retained on each sieve are collected separately 5- Determine the mass of soil retained on each sieve (i.e., M1, M2, · · · Mn) and in the Pan 6- Determine the total mass of the soil: M1 M2 · · · Mi · · · Mn Mp M 7- Determine the cumulative mass of soil retained above each sieve. For the ith sieve, it is M1 M2 · · · Mi

Once the percent finer for each sieve is calculated , the calculations are plotted on semilogarithmic graph paper with percent finer as the ordinate (arithmetic scale) and sieve opening size as the abscissa (logarithmic scale). This plot is referred to as the particle-size distribution curve.

4.3.1 Particle-Size Distribution Curve

A particle-size distribution curve can be used to determine the following parameters for a given soil: 1. Uniformity coefficient (Cu): This parameter is defined as:

2. Coefficient of gradation (Cc): This parameter is defined as:

Effective sizes D10, D30 and D60 : are the diameters in the particle-size distribution curve corresponding to 10%, 30% and 60% finer respectively.

For example :

According to USCS standards, the gravel is well graded if: cu > 4; 1< cc <3

whereas the sand is well graded if: cu > 6; 1< cc <3

4.4 Hydrometer Analysis Hydrometer analysis is used for fine grained soils passing the #200 sieve (Size <0.075mm), it is based on the principle of sedimentation of soil grains in water. When a soil specimen is dispersed in water, the particles settle at different velocities, depending on: • Size of particles • Specific gravity of particles • The viscosity of the water. For simplicity, it is assumed that all the soil particles are spheres and that the velocity of soil particles can be expressed by Stokes’ law, according to which

Table 4.2

Tables 4.2 Values of K

4.4.1 Procedure

insert the hydrometer in

the cylinder and get the reading

“ΔR”

insert the hydrometer in the cylinder and get

the readings “R” at different

timing

• Sodium hexametaphosphate generally is used as the dispersing agent.

• As the soil particles settle out of suspension the specific gravity of the mixture reduces.

• An hydrometer is used to record the variation of specific gravity with time.

• When a hydrometer is placed in the soil suspension at a time t, measured from the start of sedimentation it measures the specific gravity in the vicinity of its bulb at a depth L

• L is the depth measured from the surface of the water to the center of gravity of the hydrometer bulb at which the density of the suspension is measured.

The value of L will change with time t. • By making use of Stoke’s Law, which relates the velocity of a free falling sphere

to its diameter, the test data is reduced to provide particle diameters and the % by weight of the sample finer than a particular particle size.

Adding that:

Hydrometer test corrections:

A- Miniscus : take the reading “R” at top of miniscus then correct it by R’ = R +1 B- Specific Gravity: The hydrometer is calibrated for soils that have a specific gravity, Gs =2.65; for soils of other specific gravity, a correction “a” must be

made.(table 4.4)

C- Temperature correction

D- Deflocculant Agent: this changes the zero reading

The correction for the reading is : R – ΔR

Where Ms = mass of solids in suspension

Percent finer = 100* a (R-ΔR+FT)/Ms Percent finer = 100* a (R-ΔR+FT)/Ms Then,

R’ = R +1

Table 4.4

Unified Graph

Example : for Gs = 2.75 and T = 28o the following readings were taken from hydrometer test

Note that : to plot a combined graph for percent finer versus grain size distribution obtained from both sieve analysis and hydrometer analysis, the percent finer calculated from the sieve analysis for a given grain size does not match that calculated from the hydrometer test. The grain sizes obtained from a sieve analysis are the least sizes of soil grains, and the grain sizes obtained from the hydrometer analysis are the diameters of equivalent spheres of soil grains. Thus ,the percent finer of column 4 should be corrected as follows: